# Metacentric height

1. Jun 20, 2012

### Gavroy

hi

i am on to understand when ships are in a stable position. now i found that this is directly linked to a quantity called the metacentric height?

there are two major forces, the gravitational and the buoyant force. and in classical mechanics when i wanted to find out the torque that results from two forces i looked at the distance between them and when they where parallel and equal in magnitude torque was given by D= r x F

for which reason do i look at this metacentric height, it does not seem plausible to me at all, can somebody say a few words about why you look at this distance and not the direct distance between the two forces?

2. Jun 20, 2012

### haruspex

The trouble with the forces in flotation is that they shift around. Stability is about response to small changes. If a boat rolls in the water, it's obvious where its centre of mass moves to, but it can be less obvious how the centre of buoyancy moves.
Consider some simple case:
- hemispherical hull
The profile of the hull in the water does not change, so the centre of buoyancy remains below the centre of curvature. This makes it stable; if the hull has tilted to the right then the mass centre is now left of a vertical through the centre of curvature.
- tall pole, vertical
This is obviously unstable. When exactly vertical there is no torque, but the slightest perturbation will lead to a torque tending to accelerate the perturbation.

A critical consideration is the cross-section of the hull at the water level. Metacentric height encapsulates this.